A113444 a(n) = a(n-1) + Sum_{0<k<=n/5} a(n-5k) with a(0)=1.

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 13, 18, 24, 31, 43, 60, 83, 113, 151, 206, 283, 389, 532, 721, 982, 1342, 1837, 2512, 3422, 4665, 6367, 8699, 11886, 16218, 22126, 30195, 41226, 56299, 76849, 104883, 143147, 195404, 266776, 364175, 497092, 678503, 926164

Offset

0,6

Comments

If presented in five rows a(5n) a(5n+1).. a(5n+4) each term is the sum of the previous term in the sequence and the partial sum of its row.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,-1).

Formula

G.f.: (1-x^5)/(1-x-2*x^5+x^6).

a(n) = a(n-1) + 2*a(n-5) - a(n-6).

a(n) = 11*a(n-5) -45*a(n-10) +90*a(n-15) -90*a(n-20) +37*a(n-25)-a(n-30).

Mathematica

CoefficientList[Series[(1 - x^5)/(1 - x - 2*x^5 + x^6), {x, 0, 50}], x] (* G. C. Greubel, Mar 11 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1-x^5)/(1-x-2*x^5+x^6)) \\ G. C. Greubel, Mar 11 2017

Crossrefs

Cf. A113435, A113439, A028495.

Sequence in context: A017833 A114044 A351724 * A228669 A308020 A200444

Adjacent sequences: A113441 A113442 A113443 * A113445 A113446 A113447

Keyword

nonn,easy

Author

Floor van Lamoen, Nov 04 2005

Status

approved